Aliev R.A., Guirimov B.G. Type-2 Fuzzy Neural Networks and Their Applications

Springer, 2014. — 203 p.Ordinary neuro-fuzzy systems (i.e.
type:1 neuro-fuzzy systems) have been successfully used in a wide range of applications. To design ordinary neuro-fuzzy systems, knowledge of human experts and experimental data are needed for construction of fuzzy rules and membership functions based on available linguistic or numeric information. However, in many cases the available information or data are associated with various types of uncertainty which should be taken into account.
This uncertainty can be captured well by using higher order fuzzy sets. Hence, an effective way is to employ type-2 fuzzy sets, which augment fuzzy models with expressive power to develop models that efficiently capture the factor of uncertainty. In this regards, fuzzy type-2 neuro-fuzzy systems can represent and handle uncertain information more effectively than fuzzy type-1 neuro-fuzzy systems and contribute to the robustness and stability of the inference.
Type:2 fuzzy sets having offered additional degrees of freedom in combination with neural networks being viewed as parallel computational models with adaptive nature make it possible to directly and more effectively account for model’s uncertainties produced by different sources. The concept of type-2 fuzzy sets was initially created by Prof. L. Zadeh as an extension of ordinary fuzzy sets. Then Mendel and Karnik have developed a theory of type-2 fuzzy systems.
In spite of the intensive development of theory and design methods of type-2 neuro-fuzzy systems, the concept of type-2 neuro-fuzzy system is still in its initial stages of crystallization. There is little progress in the area of type-2 fuzzy rule extraction, merging type-2 fuzzy logic system with other constituents of soft computing, namely, with evolutionary computing, etc.
In this view, this book deals with the theory, design principles, and application of hybrid intelligent systems using type-2 fuzzy sets in combination with other paradigms of soft computing technology such as neuro-computing and evolutionary computing.Fuzzy Sets
Evolutionary Computing and Type-2 Fuzzy Neural Networks
Type-1 and Type-2 Fuzzy Neural Networks
Type-2 Fuzzy Clustering
Application of Type-2 Fuzzy Neural Networks